If the function f(x) = a|π−x| + 1, x ≤ 5; b|π−x| + 3, x > 5 is continuous at x = 5, then the value of a−b is:

For the function to be continuous at x = 5, the left-hand limit and the right-hand limit must be equal to the function value at x = 5.

Left-hand limit:
lim_(x→5⁻) f(x) = a|π−5| + 1 = a(5−π) + 1

Right-hand limit:
lim_(x→5⁺) f(x) = b|π−5| + 3 = b(5−π) + 3

Since the function is continuous at x = 5, the left-hand limit and the right-hand limit must be equal:
a(5−π) + 1 = b(5−π) + 3

Solving for a−b:
a(5−π) − b(5−π) = 2
(a−b)(5−π) = 2
a−b = 2/(5−π) = 2/(5−π) * (5+π)/(5+π) = 2(5+π)/(25−π²)
This doesn't match any of the given options. Let's reconsider the limits.

Left-hand limit:
lim_(x→5⁻) f(x) = a|π - 5| + 1 = a(5 - π) + 1

Right-hand limit:
lim_(x→5⁺) f(x) = b|π - 5| + 3 = b(5 - π) + 3

For continuity at x=5:
a(5 - π) + 1 = b(5 - π) + 3
(a - b)(5 - π) = 2
a - b = 2 / (5 - π)

Let's check the options:
If a - b = 25 - π, then (25 - π)(5 - π) = 2 which is not true.
If a - b = 2π + 5, then (2π + 5)(5 - π) = 2 which is not true.
If a - b = -2 + π + 5 = 3 + π, then (3 + π)(5 - π) = 2 which is not true.
If a - b = 2π - 5, then (2π - 5)(5 - π) = 2 which is not true.

There must be a mistake in the problem statement or the given options.